Question

If an object is thrown at an angle of 30° with the horizontal with the speed 10 meter / second, it covers horizontal distance r. What will be the horizontal distance covered if the angle is made double and speed is kept constant.

Answer 1

As we know that horizontal range
$= \frac{ {u}^{2} \times sin \: 2 \: theta}{2g}$
then as given
u = 10m/s
angle 1 from horizontal = 30°
angle 2 from horizontal = 60°
range 1 = r

then
$\frac{ {10}^{2} \times sin60 }{2g} = r \\ \\ = > \frac{100 \times \sqrt{3} }{4g} = r$
And when by angle 2

$\frac{ {10}^{2} \times sin120 }{2g} = x \\ \\ = > \frac{100 \times \sqrt{3} }{4g}$
as
from above
equation 1 = 2

then X = r

hope it helps